Question

Trace curve y^2(a-x)=x^3
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Answer 1

Answer:

The curve y²(a - x) = x³ passes through origin and symmetric about x-axis.

Step-by-step explanation:

The shape of a curve can either be closed or open. Straight lines, hyperbolas, and parabolas are a few of the open curves. Equations can be used to depict these curves in the cartesian plane. See if we can accomplish it.

Equations can be used to express a curve in a graph.

In the cartesian plane, a parabola is represented by the equation y = ax².

The general equation for an ellipse is ax² + by² = c. We obtain the equation for a circle when a and b are equal.

Given, the curve is y²(a - x) = x³ , a>0

when x = 0, then we get from the above equation, y = 0

This indicates that the curve is passes through origin.

y =  (x³/(a - x))^1/2,

This gives curve symmetrical to x-axis.

LHS is favourable. RHS turns negative if x is negative or if x exceeds 2a. As a result, the curve is limited to the range of 0 to 2a. If x > 2a, y > 0. As a result, the curve's asymptote is the line at x = 2a.

To learn more about hyperbolas, click on the link below:

https://brainly.in/question/55379010

To learn more about the symmetry, click on the link below:

https://brainly.in/question/54147130

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